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Symmetries and conserved quantities in Lindblad master equations
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This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations of unitary quantum mechanics, extending the intuition of symmetries and conserved quantities to the dissipative case. We combine and apply various results to obtain an exhaustive characterization of the infinite-time behavior of Lindblad evolution, including both the structure of the infinite-time density matrix and its dependence on initial conditions. The effect of the environment in the infinite-time limit can therefore be tracked exactly for arbitrary state initialization and without knowledge of dynamics at intermediate time. As a consequence, sufficient criteria for determining the steady state of a Lindblad master equation are obtained. These criteria are knowledge of the initial state, a basis for the steady-state subspace, and all conserved quantities. We give examples of two-qubit dissipation and single-mode $d$-photon absorption where all quantities are determined analytically. Applications of these techniques to quantum information, computation, and feedback control are discussed.
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“For many complex problems in quantum mechanics, the Liouville space formalism turns out to be very effective in finding solutions or mathematically characterizing the problem.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [2]
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“This means that | ρ ( ∞ ) 〉 〉 is a linear combination of those {| ζ k 〉 〉} with Re[ λ k ] = 0 [2, 5, 48].”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [2]
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Spectral theory of Liouvillians for dissipative phase transitions
Minganti, F., Biella, A., Bartolo, N., & Ciuti, C. (2018) · Physical Review A · doi:10.1103/physreva.98.042118 · Cited by 413
Metadata
- Authors
- Albert, V. V., & Jiang, L.
- Affiliations
- Yale University (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2014-02-21
- Volume
- 89
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2044042033
- Cited by
- 448
- References
- 117
- Citations by year
- 2026: 56 · 2025: 72 · 2024: 60 · 2023: 44 · 2022: 43 · 2021: 39 · 2020: 49 · 2019: 29 · 2018: 19 · 2017: 11 · 2016: 12 · 2015: 8 · 2014: 6
- FWCI
- 6.14
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- Lindblad master equation, steady state, first integrals, quantum symmetries, dissipative quantum systems, quantum feedback control, quantum information
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